HELP NEEDED, GIVING BRAINLIEST!Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points. Identify and describe the transformation.D: ( x, y ) ---> ( 4x, 4y ) A ( 2, 1 ), B ( 4, 1 ), C ( 4, -3 ) A. This is a dilation about (0, 0) with a scale factor of 0.25; A'(8, 4), B' (16, 4), C' (16, -12).B. This is a dilation about (0, 0) with a scale factor of 4; A'(8, 4), B' (16, 4), C' (16, -12).C. This is a dilation about (0, 0) with a scale factor of 0.25; A'(0.5, 0.25), B, (1, 0.25), C' (1, - 0.75). D. This is a dilation about (0, 0) with a scale factor of 4; A'(0.5, 0.25), B'(1, 0.25), C'(1, -0.75)

The correct answer is:B. This is a dilation about (0, 0) with a scale factor of 4; A'(8, 4), B' (16, 4), C' (16, -12).Step-by-step explanation:GivenDilation: D : (x,y) => (4x,4y)And VerticesA ( 2, 1 ), B ( 4, 1 ), C ( 4, -3 )Applying dilation on all vertices[tex]A ( 2, 1 ) => A'(4*2, 4*1) => A'(8,4)\\B ( 4, 1 ) = > B' (4*4 ,4*1) = > B'(16,4)\\C(4,-3) => C' (4*4 , 4*-3) => C'(16, -12)[/tex]To find the scale factor,As we are multiplying each vertex coordinate by 4, the dilation factor is 4.Moreover,[tex]\frac{A'}{A} = \frac{(8,4)}{(2,1)} = (4,4)[/tex]Hence the scale factor is 4.So,The correct answer is:B. This is a dilation about (0, 0) with a scale factor of 4; A'(8, 4), B' (16, 4), C' (16, -12).Keywords: Dilation, Scale factorLearn more about dilation at:brainly.com/question/10435836brainly.com/question/10541435#LearnwithBrainly